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A215060 Triangle read by rows, e.g.f. exp(x*(z+1/2))/((exp(3*x/2) + 2*cos(sqrt(3)*x/2))/3). 5
1, 0, 1, 0, 0, 1, -1, 0, 0, 1, 0, -4, 0, 0, 1, 0, 0, -10, 0, 0, 1, 19, 0, 0, -20, 0, 0, 1, 0, 133, 0, 0, -35, 0, 0, 1, 0, 0, 532, 0, 0, -56, 0, 0, 1, -1513, 0, 0, 1596, 0, 0, -84, 0, 0, 1, 0, -15130, 0, 0, 3990, 0, 0, -120, 0, 0, 1, 0, 0, -83215, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,12

LINKS

Table of n, a(n) for n=0..69.

FORMULA

Matrix inverse is A215061.

T(n,k) = A215064(n,k) - A215062(n,k) + [n==k].

|T(3*n,0)| = A002115(n).

EXAMPLE

[0] [1]

[1] [0, 1]

[2] [0, 0, 1]

[3] [-1, 0, 0, 1]

[4] [0, -4, 0, 0, 1]

[5] [0, 0, -10, 0, 0, 1]

[6] [19, 0, 0, -20, 0, 0, 1]

[7] [0, 133, 0, 0, -35, 0, 0, 1]

[8] [0, 0, 532, 0, 0, -56, 0, 0, 1]

[9] [-1513, 0, 0, 1596, 0, 0, -84, 0, 0, 1]

PROG

(Sage)

def triangle(f, dim):

    var('x, z')

    s = f.series(x, dim+2)

    P = [factorial(i)*s.coefficient(x, i) for i in range(dim)]

    for k in range(dim): print([k], [P[k].coefficient(z, i) for i in (0..k)])

def A215060_triangle(dim) :

    var('x, z')

    f = exp(x*(z+1/2))/((exp(3*x/2)+2*cos(sqrt(3)*x/2))/3)

    return triangle(f, dim)

A215060_triangle(12)

CROSSREFS

Cf. A215061, A215062, A215063, A215064, A215065.

Sequence in context: A335510 A331438 A215061 * A096623 A171914 A200627

Adjacent sequences:  A215057 A215058 A215059 * A215061 A215062 A215063

KEYWORD

sign,tabl

AUTHOR

Peter Luschny, Aug 01 2012

STATUS

approved

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Last modified May 17 06:30 EDT 2021. Contains 343965 sequences. (Running on oeis4.)